Sequential Experimental Design Research Articles

An experimental design-based approach for modelling of weapon engagement zone of an air-to-air missile

ABSTRACT It is vital for pilots to have precise information about missile ranges during air-to-air combat. The Weapon Engagement Zone (WEZ), or Dynamic Launch Zone (DLZ) for air missions, represents these ranges based on the flight conditions of both the launching and target aircraft. Generating accurate, real-time WEZ functions requires high-fidelity simulations under various engagement scenarios. Classical approaches often require numerous simulations due to uncertainty in sample requirements and complexities like nonlinearities. To address this, the study proposes a method that treats WEZ modeling as a computer experiment, using a surrogate model developed through sequential experimental design and deep neural networks (DNN). This iterative approach optimizes the number of simulations needed, minimizing the loss of model accuracy. The method’s effectiveness is validated by comparing it to classical factorial designs, showing that the proposed approach achieves similar accuracy with significantly fewer sample points, making it a more efficient solution for WEZ modeling.

Bayesian Sequential Design of Computer Experiments for Quantile Set Inversion

We consider an unknown multivariate function representing a system—such as a complex numerical simulator—taking both deterministic and uncertain inputs. Our objective is to estimate the set of deterministic inputs leading to outputs whose probability (with respect to the distribution of the uncertain inputs) of belonging to a given set is less than a given threshold. This problem, which we call Quantile Set Inversion (QSI), occurs for instance in the context of robust (reliability-based) optimization problems, when looking for the set of solutions that satisfy the constraints with sufficiently large probability. To solve the QSI problem we propose a Bayesian strategy, based on Gaussian process modeling and the Stepwise Uncertainty Reduction (SUR) principle, to sequentially choose the points at which the function should be evaluated to efficiently approximate the set of interest. We illustrate the performance and interest of the proposed SUR strategy through several numerical experiments.

Optimal Molecular Design: Generative Active Learning Combining REINVENT with Precise Binding Free Energy Ranking Simulations.

Active learning (AL) is a specific instance of sequential experimental design and uses machine learning to intelligently choose the next data point or batch of molecular structures to be evaluated. In this sense, it closely mimics the iterative design-make-test-analysis cycle of laboratory experiments to find optimized compounds for a given design task. Here, we describe an AL protocol which combines generative molecular AI, using REINVENT, and physics-based absolute binding free energy molecular dynamics simulation, using ESMACS, to discover new ligands for two different target proteins, 3CLpro and TNKS2. We have deployed our generative active learning (GAL) protocol on Frontier, the world's only exa-scale machine. We show that the protocol can find higher-scoring molecules compared to the baseline, a surrogate ML docking model for 3CLpro and compounds with experimentally determined binding affinities for TNKS2. The ligands found are also chemically diverse and occupy a different chemical space than the baseline. We vary the batch sizes that are put forward for free energy assessment in each GAL cycle to assess the impact on their efficiency on the GAL protocol and recommend their optimal values in different scenarios. Overall, we demonstrate a powerful capability of the combination of physics-based and AI methods which yields effective chemical space sampling at an unprecedented scale and is of immediate and direct relevance to modern, data-driven drug discovery.

New approaches for solubilization of phosphate rocks through solid-state fermentation by optimization of oxalic acid production

This study explores the enhancement of phosphate rock (PR) solubilization through solid-state fermentation (SSF) by optimizing oxalic acid production using Aspergillus niger. Key process parameters, including the use of agro-industrial by-products (sugarcane bagasse (SCB), wheat bran (WB), soybean bran (SB)), pH levels, sucrose supplementation, and methanol addition, were systematically evaluated through sequential experimental designs. The results identified SCB and SB in a 1:1 ratio as the most effective substrate. Remarkably, the inclusion of methanol (7 %) and sucrose (0.5 %) resulted in a 3-fold increase in oxalic acid production. Under these optimized conditions, significant phosphorus solubilization of Bayóvar, Itafós, and Registro PRs was achieved, with Bayóvar rock releasing up to 12.1 g/kgds of soluble P (63.8 % efficiency). Additionally, the SSF process effectively released organic phosphorus from the agro-industrial substrates. These findings hold promise for advancing the bio-based economy and developing future industrial biofertilizers.

Optimization of Yucca filamentosa fiber based graft copolymer through response surface methodology and evaluation of physico-chemical properties

The study of the physico-chemical modification of Yucca filamentosa (Yf) natural fiber by graft copolymerization with ethylmethacrylate using ferrous ammonium sulfate-potassium persulfate as a redox initiator has been reported in the article. Initially, six process parameters; reaction duration, reaction temperature, solvent amount, pH, FAS:KPS ratio, and monomer concentration were used in the study in a sequential experimental design technique, and the significant process variables affecting the yield of the graft copolymer were identified. The Resolution-V design method identified the significant parameters as the reaction temperature, amount of solvent, and the concentration of monomer. In second phase of the study, the screened variables were utilized in the development of a model through the technique of response surface methodology (RSM) for the prediction of the yields, and its optimization. The developed RSM model fitted well with the experimental data, and predicted for the optimal conditions of reactions as temperature 50 °C, solvent 100 ml, and the monomer 3.05 × 10−3 mol/L; at which the highest graft yield percentage obtained was 124.2%. The techniques of FTIR, SEM, and XRD were used for the characterization graft copolymers. Studies of the various physico-chemical properties showed that the produced graft copolymers were more resistant than the natural fibers.

Cultivation of a naturally resilient Chlorella sp.: A bioenergetic strategy for valorization of cheese whey for high nutritional biomass production

This study investigated Chlorella's capacity to treat cheese whey (CW) effluent and produce a high-nutritional value biomass, by using a systematic sequential experimental design. Physicochemical analysis of CW revealed its high pollution load, characterized by elevated levels of lactose, phosphorus, and nitrogen, as well as high turbidity due to the presence of whey solids. Screening experiments demonstrated that trace mineral addition and continuous air supply are essential factors for Chlorella biomass production in CW (>800 mg·mL−1). Furthermore, whey solids did not hinder Chlorella growth, with notable biomass production observed even in undiluted CW, demonstrating this microalga's ability to adapt metabolically to the complex environment. Laboratory-scale photobioreactor experiments confirmed Chlorella's ability to produce biomass in CW, outperforming controls (>800 mg·mL−1). Bioremediation potential assessment exhibited significant reductions in organic pollutants (>14 g·L−1 COD), nitrogen (>400 mg·L−1), phosphorus (>140 mg·L−1) and sodium (>650 mg·L−1). CW solids were also removed with Chlorella harvesting (>99 %). Harvested algal biomass was enriched with proteins (>40 g·100 g−1), polyunsaturated fatty acids (>9 % TFA) and pigments, offering potential applications in nutraceutical and pharmaceutical industries. Overall, this study highlights Chlorella's efficacy in CW treatment and biomass valorization, offering a sustainable solution for dairy wastewater management while producing valuable resources.

Guided experimental design for static nonparametric modeling

Sequential or goal-oriented experimental design methods help achieve the target cheaply and quickly. In this work, we exploit Bayesian Optimization to obtain accurate and reliable static models for physical phenomena in cases where parametric models are unavailable. Our Guided Design of Experiments (G-DoE) workflow is proposed with a purely explorative acquisition function and an empirical stopping criterion. Two stopping criteria are proposed, one that is based on convergence rates of the prediction uncertainty and another that is based on a tolerance limit. Stopping criteria thresholds are established by studying factors like noise level and dimension size and their impact on prediction uncertainty convergence. Furthermore, we compare the G-DoE framework with classical Full Factorial and Response Surface strategies in terms of the suggested number of experiments and corresponding accuracy of fit. The proposed algorithm is tested using a methanol synthesis reaction experiment, a vapor pressure experiment, and a synthetic example.

Exploring the potentialities of a biodegradable polymeric film in sample preparation: An optimized “white” protocol to extract and quantify emerging contaminants in water

BackgroundThe introduction of white analytical chemistry encourages the development of methods characterized by a balance among greenness, productivity/feasibility and analytical performances. In the environmental analysis of emerging contaminants (ECs), for which high sensitivity and specificity are mandatory, the use of green and sustainable sample preparation needs to be coupled to a reliable analytical determination. Herein, an extraction method based on the use of a biodegradable polymeric film (Mater-Bi) and coupled to LC-MS/MS analysis was developed for the sensitive determination of ECs in wastewater. ResultsThe interaction among a range of ECs and the Mater-Bi film (a commercially available patented blend of polybutylene-terephthalate, starch and fatty acids) was investigated by two sequential experimental designs, to simultaneously study several factors and optimize extraction efficiency. The final method, resembling a fabric phase sorptive extraction, involved pH and ionic strength modification of the sample, 1h extraction and desorption in ethanol. Satisfactory recoveries from real wastewater were obtained for sixteen analytes (56–116 %), as well as excellent precision (inter-day relative standard deviations below 10 % for most compounds). Matrix effect was in the range 88–116 % at the lower pre-concentration factor, but also acceptable in most cases at the higher pre-concentration factor. LODs in matrix, from 0.004 to 0.159 μg L−1, were lower than or comparable to those from recent studies employing green extraction procedures. The method demonstrated its applicability to samples from wastewater treatment plants, allowing quantification of pharmaceuticals and UV filters at the μg L−1 and ng L−1 levels, respectively. SignificanceFor the first time, the synthetic biopolymer Mater-Bi, so far unexplored for the use in analytical chemistry, was exploited for a green, simple and extremely cheap extraction protocol. The optimized method is suitable for several ECs, guaranteeing very good accuracy, precision and specificity, also thanks to the LC-MS/MS analysis. The evaluation by green and white analytical chemistry metrics highlighted its superiority to conventional extraction methods.

Prevalence of current chronic pain in Royal Canadian Mounted Police cadets

ABSTRACT Background Nearly half of active duty Royal Canadian Mounted Police (RCMP) officers report experiencing current chronic pain (43%; i.e. pain lasting longer than 3 months). Most RCMP officers who report chronic pain indicate that the pain started after working as RCMP officers (91%). Baseline data on chronic pain prevalence among RCMP cadets has not been available. Aims The current study was designed to provide cross-sectional estimates of chronic pain prevalence among RCMP cadets starting the Cadet Training Program and to assess for sociodemographic differences among participants. Methods The RCMP Study uses a longitudinal prospective sequential experimental cohort design to create a clustered randomized trial that engages individual participants for 5.5 years. The current article provides cross-sectional associations between chronic pain prevalence and sociodemographic characteristics. Participants were RCMP cadets starting the Cadet Training Program (n = 770). Location, intensity (on a 0–10 scale and days per week experienced), and duration (number of months) of chronic pain were reported. Differences across sociodemographic characteristics were examined. Results Few RCMP cadets reported experiencing chronic pain (10%); lower back pain was rated as the most severe in terms of intensity and duration and second most frequently reported in number of days experienced per week. Prevalence of chronic pain was lower among RCMP cadets than among RCMP officers. Conclusions Chronic pain prevalence among active duty RCMP officers may result from or be moderated by operational duties, as well as routine aging. Future researchers could examine ways to mitigate chronic pain development during RCMP officer careers.

Investigation of Deposition Parameters for Near-Beta Alloy Ti-55511 Fabricated by Directed Energy Deposition

The directed energy deposition (DED) parameters were determined for near-β alloy Ti-55511 by employing statistical design of experiments (DOEs) methods. Parameters resulting in fully dense freeform deposits were identified using two sequential DOEs. Single laser tracks were printed with several laser power, traverse rate, and powder feed rate settings in an initial DOE to identify promising build parameters. The capture efficiency and effective deposition rate were used to characterize and rank the single track deposits. The best parameters were then used to print a solid cube with various X–Y and Z overlaps (different hatch spacing, HS, and layer thickness, ZS) in a second DOE. Suitable deposition parameters were selected based on the cube density and microstructure and were used to fabricate larger tensile samples for mechanical testing. Multiple parameter sets were found to provide dense Ti-55511 deposits with acceptable mechanical properties and the parametric models showed statistical significance.

Bayesian reinforcement learning reliability analysis

A Bayesian reinforcement learning reliability method that combines Bayesian inference for the failure probability estimation and reinforcement learning-guided sequential experimental design is proposed. The reliability-oriented sequential experimental design is framed as a finite-horizon Markov decision process (MDP), with the associated utility function defined by a measure of epistemic uncertainty about Kriging-estimated failure probability, referred to as integrated probability of misclassification (IPM). On this basis, a one-step Bayes optimal learning function termed integrated probability of misclassification reduction (IPMR), along with a compatible convergence criterion, is defined. Three effective strategies are implemented to accelerate IPMR-informed sequential experimental design: (i) Analytical derivation of the inner expectation in IPMR, simplifying it to a single expectation. (ii) Substitution of IPMR with its upper bound IPMRU to avoid element-wise computation of its integrand. (iii) Rational pruning of both quadrature set and candidate pool in IPMRU to alleviate computer memory constraint. The efficacy of the proposed approach is demonstrated on two benchmark examples and two numerical examples. Results indicate that IPMRU facilitates a much more rapid reduction of IPM compared to other existing learning functions, while requiring much less computational time than IPMR itself. Therefore, the proposed reliability method offers a substantial advantage in both computational efficiency and accuracy, especially in complex dynamic reliability problems.

Optimisation of DNA electroporation protocols for different plant-associated bacteria

Electroporation is a vital process that facilitates the use of modern recombineering and other high-throughput techniques in a wide array of microorganisms, including non-model bacteria like plant growth-promoting bacteria (PGPB). These microorganisms play a significant role in plant health by colonizing plants and promoting growth through nutrient exchange and hormonal regulation. In this study, we introduce a sequential Design of Experiments (DOE) approach to obtain highly competent cells swiftly and reliably for electroporation. Our method focuses on optimizing the three stages of the electroporation procedure—preparing competent cells, applying the electric pulse field, and recovering transformed cells—separately. We utilized a split-plot fractional design with five factors and a covariate to optimize the first step, response surface methodology (RSM) for the second step, and Plackett-Burman design for two categorical factors and one continuous factor for the final step. Following the experimental sequence with three bacterial models, we achieved efficiencies 10 to 100 times higher, reaching orders of 105 to 106 CFU/μg of circular plasmid DNA. These results highlight the significant potential for enhancing electroporation protocols for non-model bacteria.

Towards informatics-driven design of nuclear waste forms

Informatics-driven approaches, such as machine learning and sequential experimental design, have shown the potential to drastically impact next-generation materials discovery and design.

Structural reliability analysis based on probability density evolution method and stepwise truncated variance reduction

To address the substantial computational burden associated with probability density evolution method (PDEM) in structural reliability analysis, this study proposes a novel look-ahead learning function named stepwise truncated variance reduction (STVR), integrating polynomial chaos Kriging (PCK) and PDEM. Three key features of STVR are highlighted. First, it enables quantifying the maximum reduction in predictive errors of PCK within the regions of interest (ROI) when adding a new point. Second, closed-form expression for STVR is derived through Kriging update formulas, eliminating the need for computationally intensive Gauss–Hermite quadrature or extensive conditional simulations of PCK. Third, a dynamic adjustment procedure is proposed for the probability level-related parameter in STVR, with the aim of achieving a good balance between the exploitation and exploration of ROI during the sequential experimental design process. The performance of STVR is demonstrated through two benchmark analytical functions and three numerical examples of varying complexity. Results indicate that the dynamic adjustment procedure for the probability level-related parameter in STVR outperforms the empirical setting of a minor value. Then, STVR proves more advantageous than existing pointwise and look-ahead learning functions, particularly in addressing complex dynamic reliability problems.

Integrating a tailored recurrent neural network with Bayesian experimental design to optimize microbial community functions.

Microbiomes interact dynamically with their environment to perform exploitable functions such as production of valuable metabolites and degradation of toxic metabolites for a wide range of applications in human health, agriculture, and environmental cleanup. Developing computational models to predict the key bacterial species and environmental factors to build and optimize such functions are crucial to accelerate microbial community engineering. However, there is an unknown web of interactions that determine the highly complex and dynamic behavior of these systems, which precludes the development of models based on known mechanisms. By contrast, entirely data-driven machine learning models can produce physically unrealistic predictions and often require significant amounts of experimental data to learn system behavior. We develop a physically-constrained recurrent neural network that preserves model flexibility but is constrained to produce physically consistent predictions and show that it can outperform existing machine learning methods in the prediction of certain experimentally measured species abundance and metabolite concentrations. Further, we present a closed-loop, Bayesian experimental design algorithm to guide data collection by selecting experimental conditions that simultaneously maximize information gain and target microbial community functions. Using a bioreactor case study, we demonstrate how the proposed framework can be used to efficiently navigate a large design space to identify optimal operating conditions. The proposed methodology offers a flexible machine learning approach specifically tailored to optimize microbiome target functions through the sequential design of informative experiments that seek to explore and exploit community functions.

Sequential Bayesian Experimental Design for Calibration of Expensive Simulation Models

Simulation models of critical systems often have parameters that need to be calibrated using observed data. For expensive simulation models, calibration is done using an emulator of the simulation model built on simulation output at different parameter settings. Using intelligent and adaptive selection of parameters to build the emulator can drastically improve the efficiency of the calibration process. The article proposes a sequential framework with a novel criterion for parameter selection that targets learning the posterior density of the parameters. The emergent behavior from this criterion is that exploration happens by selecting parameters in uncertain posterior regions while simultaneously exploitation happens by selecting parameters in regions of high posterior density. The advantages of the proposed method are illustrated using several simulation experiments and a nuclear physics reaction model.

Phosphorus Recovery from Wastewater Aiming Fertilizer Production: Struvite Precipitation Optimization Using a Sequential Plackett–Burman and Doehlert Design

The precipitation of struvite from wastewater is a potential alternative for the recovery of nutrients, especially phosphorus, which is an essential macronutrient for agriculture but can be harmful to the environment when improperly disposed of in water bodies. In addition, struvite has elements of great added value for agricultural activity (P, N, and Mg) and is, therefore, considered a sustainable alternative fertilizer. In its formation process, several intervening physicochemical factors may be responsible for the production yield levels. Optimization processes can help to define and direct the factors that truly matter for precipitation. In this context, a sequential design of experiments (DOE) methodology was applied to select and optimize the main struvite precipitation factors in wastewater. Initially, a screening was performed with eight factors with the aid of Plackett–Burman design, and the factors with a real influence on the process were identified. Then, a Doehlert design was used for optimization by applying the response surface methodology and the desirability function. The results were used to identify the optimal points of the pH (10.2), N/P ratio (≥4), and initial phosphorus concentration (183.5 mg/L); these values had a greater effect on phosphorus recovery and the production of struvite, which was confirmed through thermochemical analysis of the decomposition of its structure by differential scanning calorimeter—glass transition temperature (DSC-TG) and phase identification by X-ray diffraction (XRD). The determination of the best synthesis conditions is an enormous contribution to the control of the process because these conditions lead to better yields and higher levels of phosphorus recovery.

Bayesian sequential optimal experimental design for nonlinear models using policy gradient reinforcement learning

We present a mathematical framework and computational methods for optimally designing a finite sequence of experiments. This sequential optimal experimental design (sOED) problem is formulated as a finite-horizon partially observable Markov decision process (POMDP) under a Bayesian setting and with information-theoretic utilities. The formulation is general and may accommodate continuous random variables, non-Gaussian posteriors, and nonlinear forward models. The sOED design policy incorporates elements of feedback and lookahead simultaneously, and we show it to generalize the commonly-used batch and greedy design strategies. We solve for the sOED policy using the policy gradient (PG) method from reinforcement learning, and provide a derivation for the PG expression in the sOED context. Adopting an actor–critic approach, the policy and value functions are parameterized using deep neural networks and improved via PG estimates produced from simulated episodes of designs and observations. The new PG-sOED algorithm is first validated on a linear-Gaussian benchmark, and then compared against other design baselines on a sensor movement problem for contaminant source inversion in a convection–diffusion field. We provide explanation for the policy behaviors using knowledge of the underlying physical process.

Sequential Experiment Design Method Based on Uniformity and Distortion of Responses

Sequential Experiment Design Method Based on Uniformity and Distortion of Responses

Uncertainty Quantification and Experimental Design for Large-Scale Linear Inverse Problems under Gaussian Process Priors

We consider the use of Gaussian process (GP) priors for solving inverse problems in a Bayesian framework. As is well known, the computational complexity of GPs scales cubically in the number of datapoints. Here we show that in the context of inverse problems involving integral operators, one faces additional difficulties that hinder inversion on large grids. Furthermore, in that context, covariance matrices can become too large to be stored. By leveraging recent results about sequential disintegrations of Gaussian measures, we are able to introduce an implicit representation of posterior covariance matrices that reduces the memory footprint by only storing low rank intermediate matrices, while allowing individual elements to be accessed on-the-fly without needing to build full posterior covariance matrices. Moreover, it allows for fast sequential inclusion of new observations. These features are crucial when considering sequential experimental design tasks. We demonstrate our approach by computing sequential data collection plans for excursion set recovery for a gravimetric inverse problem, where the goal is to provide fine resolution estimates of high density regions inside the Stromboli volcano, Italy. Sequential data collection plans are computed by extending the weighted integrated variance reduction (wIVR) criterion to inverse problems. Our results show that this criterion is able to significantly reduce the uncertainty on the excursion volume, reaching close to minimal levels of residual uncertainty. Overall, our techniques allow the advantages of probabilistic models to be brought to bear on large-scale inverse problems arising in the natural sciences. Particularly, applying the latest developments in Bayesian sequential experimental design on realistic large-scale problems opens new venues of research at a crossroads between mathematical modelling of natural phenomena, statistical data science, and active learning.